The answer is: "it depends". In theory, you could use a number of different models (e.g. the infographic in Daniel Bingham's answer, John Jeavon's "How to Grow More Vegetables", etc). You'll get a wide variety of answers, and a lot depends on your specific circumstances -- and will likely vary widely for you from year to year.
Note that a limiting factor may not be so much the cold, but the fact that the plants get fewer hours of sunlight in the winter as you move to higher latitudes, so they're not growing as much in the winter. Eliot Coleman talks about this in some of his books. One strategy you can use if this is an issue is to start your plants that will be harvested during the winter in the late summer so that they can have enough time to grow before the short days of winter arrive; they will be dormant (i.e. not growing) at that point but still harvestable.
I think an appropriate strategy would be to start small and experiment to figure out what your right size is. Set up some hoops over your garden to protect a handful of different winter crops. Keep track of how much space you allocate, what you've planted, and how much you can harvest and eat. Use this information to scale up your winter protection, and possibly to make adjustments to your crop selection, management, and harvesting.
A complementary strategy would be to increase the size of your summer garden so that you can have vegetables preserved for winter use. Winter squash, potatoes, and onions all store easily, and many more vegetables can be stored for months if you can provide a proper storage facility. (Apples and other fruits too, if you take a food forest approach to gardening.) Even if you don't have a good root cellar, you can preserve many other foods in a variety of ways. If you're processing your own chickens when there's a lot of vegetables available, use them in vegetable-heavy soups. (It makes the meat stretch farther.) These soups can be canned and enjoyed all winter long. I keep bags of greens (kale, spinach, chard) in the freezer for use in recipes during the winter -- lasagna, soups, quiche, etc. If you don't like the energy used by a freezer, most of these can be dried effectively as well, and stored for long periods that way.
Finally, to put a number on it, let's say that you want to provide four 4oz salads (4oz of fresh greens only) a day for 6 months (October 1 through March 31). That's a pound a day for 180 days -- 180 pounds. A decent yield for spring-grown spinach would be about 1 pound per square foot, lettuce perhaps 2 lb/sqft. To make up a number, let's say you average about .5 lb/sqft for winter-harvested greens. You'd need a greenhouse with 360 square feet of growing space, plus space for paths, whatever heating you are going to provide, and whatever else you might keep in the building. It's a fairly simple formula, so you can play with the numbers, but until you know what your numbers really are (i.e. the strategy above), it's just a guess.
(I'm assuming greens above because they're among the easiest things for winter harvest, and to keep the answer simpler. Carrots and parsnips can be harvested in winter too as long as you keep the ground from freezing around them, but they don't need a greenhouse. I cribbed the yield numbers from Jeavons, because I had it handy.)